There's also a padding/clipping issue I can't repro easily, but it has something to do with the padding-top: 0 applied to the div#input when no-label-float is present.
Eeeek, on it. Though, from your demo, the original paper-dropdown-menu loses its dropdown in a flex layout, so that wasn't doing too great to begin with 😟
I'm seeing some differences between paper-dropdown-menu and paper-dropdown-menu-light. They have different widths in flex layouts:
https://jsfiddle.net/mgiuffrida/30wysv8m/
There's also a padding/clipping issue I can't repro easily, but it has something to do with the
padding-top: 0
applied to thediv#input
whenno-label-float
is present.